Stochastic Aspects of Magnetic Lines of Force with Application to Cosmic-Ray Propagation 论文

摘要

It is pointed out that magnetic lines of force in nature are generally stochastic and ergodic. Owing to unavoidable fluctuations in the field, adjacent lines of force random-walk away from each other. The stochastic properties of the lines of force in the astrophysical universe are related to the stochastic prop- erties of the (turbulent) velocity fields in which they are imbedded. The consequent random walk of the field lines is shown to contribute appreciably to K1, the coefficient for particle diffusion normal to the average field, with the result that the particles are spread across the average magnetic field much more rapidly than expected from the usual resonant scattering by small-scale irregularities. The Sun's extended magnetic field, traversed by both energetic solar particles and galactic cosmic rays, serves as an excellent illustration of these concepts. Application of the theory to the interplanetary magnetic fields shows that the random walk of the field lines is determined by the observed power spec- trum of the fluctuations in the magnetic field at zero frequency. The observed turbulent velocity field in the solar photosphere yields a random walk equal to that obtained from the observed power spectrum of the magnetic field. These two determinations of the random walk of the field lines, in turn, agree with the observed spread in solar longitude of promptly arriving solar cosmic rays. The observed shear planes and flux tubes of the "wet spaghetti" model of the interplanetary magnetic field are evidently a direct manifestation of the photospheric supergranulation. We also discuss the diffusion of cosmic rays in the interplanetary magnetic field observed near solar minimum. For protons with energies of 10 MeV and below, the ratio KL/KII at the orbit of the Earth becomes comparable to unity, instead of nearly zero as would be expected on the basis of resonant scat- tering alone. The contribution of the random walk to K~ is also significant at relativistic energies. Applica- tion to the theory of the diurnal variation of galactic cosmic rays agrees with observation both at `-~.-`1O MeV and at relativistic particle energies